# Non-linear Visual Knowledge Discovery with Elliptic Paired Coordinates

arXiv: https://arxiv.org/abs/2107.04974 · HTML: https://mlsanity.com/paper/2107.04974/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 13 references that are in the map.
- First posted on arXiv 11 Jul 2021.

## Builds on (most cited first, 4 of 4)

- [RuleMatrix: Visualizing and Understanding Classifiers with Rules](https://mlsanity.com/paper/1807.06228/) (2018)
- [A Survey of Visual Analytics Techniques for Machine Learning](https://mlsanity.com/paper/2008.09632/) (2020)
- [Towards Better Analysis of Machine Learning Models: A Visual Analytics Perspective](https://mlsanity.com/paper/1702.01226/) (2017)
- [Survey of explainable machine learning with visual and granular methods beyond quasi-explanations](https://mlsanity.com/paper/2009.10221/) (2020)

## Built on by (most cited first, 4 of 4)

- [Interactive Decision Tree Creation and Enhancement with Complete Visualization for Explainable Modeling](https://mlsanity.com/paper/2305.18432/) (2023)
- [Synthetic Data Generation and Automated Multidimensional Data Labeling for AI/ML in General and Circular Coordinates](https://mlsanity.com/paper/2409.02079/) (2024)
- [Full High-Dimensional Intelligible Learning In 2-D Lossless Visualization Space](https://mlsanity.com/paper/2305.19132/) (2023)
- [High-Dimensional Data Classification in Concentric Coordinates](https://mlsanity.com/paper/2507.18450/) (2025)

## Abstract (arXiv)

It is challenging for humans to enable visual knowledge discovery in data with more than 2-3 dimensions with a naked eye. This chapter explores the efficiency of discovering predictive machine learning models interactively using new Elliptic Paired coordinates (EPC) visualizations. It is shown that EPC are capable to visualize multidimensional data and support visual machine learning with preservation of multidimensional information in 2-D. Relative to parallel and radial coordinates, EPC visualization requires only a half of the visual elements for each n-D point. An interactive software system EllipseVis, which is developed in this work, processes high-dimensional datasets, creates EPC visualizations, and produces predictive classification models by discovering dominance rules in EPC. By using interactive and automatic processes it discovers zones in EPC with a high dominance of a single class. The EPC methodology has been successful in discovering non-linear predictive models with high coverage and precision in the computational experiments. This can benefit multiple domains by producing visually appealing dominance rules. This chapter presents results of successful testing the EPC non-linear methodology in experiments using real and simulated data, EPC generalized to the Dynamic Elliptic Paired Coordinates (DEPC), incorporation of the weights of coordinates to optimize the visual discovery, introduction of an alternative EPC design and introduction of the concept of incompact machine learning methodology based on EPC/DEPC.